Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:06 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a Monte Carlo
simulation study for a two-level growth
model for a continuous outcome (three-
level analysis)
MONTECARLO:
NAMES ARE y1-y4 x w;
NOBSERVATIONS = 1000;
NREPS = 500;
SEED = 58459;
CUTPOINTS = x (1) w (0);
MISSING = y1-y4;
NCSIZES = 3;
CSIZES = 40 (5) 50 (10) 20 (15);
WITHIN = x;
BETWEEN = w;
MODEL POPULATION:
%WITHIN%
x@1;
iw sw | y1@0 y2@1 y3@2 y4@3;
y1-y4*.5;
iw ON x*1;
sw ON x*.25;
iw*1; sw*.2;
%BETWEEN%
w@1;
ib sb | y1@0 y2@1 y3@2 y4@3;
y1-y4@0;
ib ON w*.5;
sb ON w*.25;
[ib*1 sb*.5];
ib*.2; sb*.1;
MODEL MISSING:
[y1-y4@-1];
y1 ON x*.4;
y2 ON x*.8;
y3 ON x*1.6;
y4 ON x*3.2;
ANALYSIS: TYPE IS TWOLEVEL;
MODEL:
%WITHIN%
iw sw | y1@0 y2@1 y3@2 y4@3;
y1-y4*.5;
iw ON x*1;
sw ON x*.25;
iw*1; sw*.2;
%BETWEEN%
ib sb | y1@0 y2@1 y3@2 y4@3;
y1-y4@0;
ib ON w*.5;
sb ON w*.25;
[ib*1 sb*.5];
ib*.2; sb*.1;
OUTPUT: TECH9 NOCHISQUARE;
INPUT READING TERMINATED NORMALLY
this is an example of a Monte Carlo
simulation study for a two-level growth
model for a continuous outcome (three-
level analysis)
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
Number of replications
Requested 500
Completed 500
Value of seed 58459
Number of dependent variables 4
Number of independent variables 2
Number of continuous latent variables 4
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4
Observed independent variables
X W
Continuous latent variables
IW SW IB SB
Variables with special functions
Within variables
X
Between variables
W
Estimator MLR
Information matrix OBSERVED
Maximum number of iterations 100
Convergence criterion 0.100D-05
Maximum number of EM iterations 500
Convergence criteria for the EM algorithm
Loglikelihood change 0.100D-02
Relative loglikelihood change 0.100D-05
Derivative 0.100D-03
Minimum variance 0.100D-03
Maximum number of steepest descent iterations 20
Maximum number of iterations for H1 2000
Convergence criterion for H1 0.100D-03
Optimization algorithm EMA
SUMMARY OF DATA FOR THE FIRST REPLICATION
Number of missing data patterns 15
Cluster information
Size (s) Number of clusters of Size s
5 40
10 50
15 20
Average cluster size 9.091
Estimated Intraclass Correlations for the Y Variables
Intraclass Intraclass Intraclass
Variable Correlation Variable Correlation Variable Correlation
Y1 0.192 Y2 0.221 Y3 0.304
Y4 0.327
SUMMARY OF MISSING DATA PATTERNS FOR THE FIRST REPLICATION
MISSING DATA PATTERNS (x = not missing)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Y1 x x x x x x x x
Y2 x x x x x x x x
Y3 x x x x x x x x
Y4 x x x x x x x x
X x x x x x x x x x x x x x x x
W x x x x x x x x x x x x x x x
MISSING DATA PATTERN FREQUENCIES
Pattern Frequency Pattern Frequency Pattern Frequency
1 242 6 31 11 35
2 46 7 75 12 26
3 50 8 90 13 25
4 117 9 95 14 31
5 82 10 45 15 10
COVARIANCE COVERAGE OF DATA FOR THE FIRST REPLICATION
Minimum covariance coverage value 0.100
PROPORTION OF DATA PRESENT
Covariance Coverage
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 0.713
Y2 0.516 0.737
Y3 0.499 0.500 0.696
Y4 0.445 0.464 0.458 0.626
X 0.713 0.737 0.696 0.626 1.000
W 0.713 0.737 0.696 0.626 1.000
Covariance Coverage
W
________
W 1.000
MODEL FIT INFORMATION
Number of Free Parameters 16
Loglikelihood
H0 Value
Mean -4424.440
Std Dev 55.422
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.992 -4553.368 -4553.248
0.980 0.986 -4538.260 -4529.117
0.950 0.966 -4515.604 -4513.658
0.900 0.898 -4495.469 -4496.800
0.800 0.784 -4471.083 -4472.463
0.700 0.678 -4453.503 -4457.876
0.500 0.488 -4424.440 -4426.009
0.300 0.310 -4395.377 -4391.965
0.200 0.208 -4377.797 -4376.545
0.100 0.114 -4353.411 -4351.576
0.050 0.052 -4333.277 -4332.209
0.020 0.018 -4310.620 -4311.383
0.010 0.006 -4295.512 -4299.992
Information Criteria
Akaike (AIC)
Mean 8880.880
Std Dev 110.844
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.994 8623.024 8628.693
0.980 0.982 8653.240 8653.822
0.950 0.948 8698.553 8693.091
0.900 0.886 8738.823 8734.600
0.800 0.792 8787.594 8784.575
0.700 0.690 8822.754 8815.366
0.500 0.512 8880.880 8883.723
0.300 0.322 8939.007 8946.980
0.200 0.216 8974.167 8976.421
0.100 0.102 9022.938 9023.993
0.050 0.034 9063.208 9057.784
0.020 0.014 9108.521 9087.750
0.010 0.008 9138.737 9129.273
Bayesian (BIC)
Mean 8959.404
Std Dev 110.844
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.994 8701.548 8707.217
0.980 0.982 8731.764 8732.346
0.950 0.948 8777.077 8771.615
0.900 0.886 8817.347 8813.124
0.800 0.792 8866.118 8863.099
0.700 0.690 8901.278 8893.890
0.500 0.512 8959.404 8962.247
0.300 0.322 9017.531 9025.505
0.200 0.216 9052.691 9054.945
0.100 0.102 9101.462 9102.517
0.050 0.034 9141.732 9136.308
0.020 0.014 9187.045 9166.274
0.010 0.008 9217.261 9207.797
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 8908.587
Std Dev 110.844
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.994 8650.731 8656.400
0.980 0.982 8680.947 8681.529
0.950 0.948 8726.260 8720.798
0.900 0.886 8766.530 8762.307
0.800 0.792 8815.301 8812.282
0.700 0.690 8850.461 8843.073
0.500 0.512 8908.587 8911.430
0.300 0.322 8966.714 8974.688
0.200 0.216 9001.874 9004.128
0.100 0.102 9050.645 9051.701
0.050 0.034 9090.915 9085.491
0.020 0.014 9136.228 9115.457
0.010 0.008 9166.444 9156.980
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
IW |
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
SW |
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 3.000 3.0000 0.0000 0.0000 0.0000 1.000 0.000
IW ON
X 1.000 1.0012 0.1227 0.1192 0.0150 0.930 1.000
SW ON
X 0.250 0.2499 0.0846 0.0797 0.0071 0.938 0.856
SW WITH
IW 0.000 0.0019 0.0335 0.0334 0.0011 0.942 0.058
Residual Variances
Y1 0.500 0.4967 0.0625 0.0645 0.0039 0.956 1.000
Y2 0.500 0.5001 0.0411 0.0401 0.0017 0.924 1.000
Y3 0.500 0.5025 0.0501 0.0479 0.0025 0.946 1.000
Y4 0.500 0.5003 0.0866 0.0863 0.0075 0.946 1.000
IW 1.000 0.9982 0.0852 0.0825 0.0072 0.938 1.000
SW 0.200 0.1992 0.0224 0.0215 0.0005 0.942 1.000
Between Level
IB |
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
SB |
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 3.000 3.0000 0.0000 0.0000 0.0000 1.000 0.000
IB ON
W 0.500 0.5037 0.1215 0.1184 0.0147 0.936 0.988
SB ON
W 0.250 0.2488 0.0759 0.0737 0.0058 0.932 0.914
SB WITH
IB 0.000 0.0005 0.0241 0.0225 0.0006 0.938 0.062
Intercepts
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
IB 1.000 1.0002 0.0826 0.0851 0.0068 0.944 1.000
SB 0.500 0.5009 0.0516 0.0523 0.0027 0.944 1.000
Residual Variances
Y1 0.000 0.0001 0.0000 0.0000 0.0000 1.000 0.000
Y2 0.000 0.0001 0.0000 0.0000 0.0000 1.000 0.000
Y3 0.000 0.0001 0.0000 0.0000 0.0000 1.000 0.000
Y4 0.000 0.0001 0.0000 0.0000 0.0000 1.000 0.000
IB 0.200 0.1919 0.0507 0.0502 0.0026 0.934 0.996
SB 0.100 0.0973 0.0202 0.0196 0.0004 0.918 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.453E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
IW SW X
________ ________ ________
Y1 0 0 0
Y2 0 0 0
Y3 0 0 0
Y4 0 0 0
X 0 0 0
THETA
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 1
Y2 0 2
Y3 0 0 3
Y4 0 0 0 4
X 0 0 0 0 0
ALPHA
IW SW X
________ ________ ________
0 0 0
BETA
IW SW X
________ ________ ________
IW 0 0 5
SW 0 0 6
X 0 0 0
PSI
IW SW X
________ ________ ________
IW 7
SW 8 9
X 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN
NU
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
IB SB W
________ ________ ________
Y1 0 0 0
Y2 0 0 0
Y3 0 0 0
Y4 0 0 0
W 0 0 0
THETA
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
Y1 0
Y2 0 0
Y3 0 0 0
Y4 0 0 0 0
W 0 0 0 0 0
ALPHA
IB SB W
________ ________ ________
10 11 0
BETA
IB SB W
________ ________ ________
IB 0 0 12
SB 0 0 13
W 0 0 0
PSI
IB SB W
________ ________ ________
IB 14
SB 15 16
W 0 0 0
STARTING VALUES FOR WITHIN
NU
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
IW SW X
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
Y3 1.000 2.000 0.000
Y4 1.000 3.000 0.000
X 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
X 0.000 0.000 0.000 0.000 0.000
ALPHA
IW SW X
________ ________ ________
0.000 0.000 0.000
BETA
IW SW X
________ ________ ________
IW 0.000 0.000 1.000
SW 0.000 0.000 0.250
X 0.000 0.000 0.000
PSI
IW SW X
________ ________ ________
IW 1.000
SW 0.000 0.200
X 0.000 0.000 0.500
STARTING VALUES FOR BETWEEN
NU
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
IB SB W
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
Y3 1.000 2.000 0.000
Y4 1.000 3.000 0.000
W 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
Y1 0.000
Y2 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
ALPHA
IB SB W
________ ________ ________
1.000 0.500 0.000
BETA
IB SB W
________ ________ ________
IB 0.000 0.000 0.500
SB 0.000 0.000 0.250
W 0.000 0.000 0.000
PSI
IB SB W
________ ________ ________
IB 0.200
SB 0.000 0.100
W 0.000 0.000 0.500
POPULATION VALUES FOR WITHIN
NU
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
IW SW X
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
Y3 1.000 2.000 0.000
Y4 1.000 3.000 0.000
X 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
X 0.000 0.000 0.000 0.000 0.000
ALPHA
IW SW X
________ ________ ________
0.000 0.000 0.000
BETA
IW SW X
________ ________ ________
IW 0.000 0.000 1.000
SW 0.000 0.000 0.250
X 0.000 0.000 0.000
PSI
IW SW X
________ ________ ________
IW 1.000
SW 0.000 0.200
X 0.000 0.000 1.000
POPULATION VALUES FOR BETWEEN
NU
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
IB SB W
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
Y3 1.000 2.000 0.000
Y4 1.000 3.000 0.000
W 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
Y1 0.000
Y2 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
ALPHA
IB SB W
________ ________ ________
1.000 0.500 0.000
BETA
IB SB W
________ ________ ________
IB 0.000 0.000 0.500
SB 0.000 0.000 0.250
W 0.000 0.000 0.000
PSI
IB SB W
________ ________ ________
IB 0.200
SB 0.000 0.100
W 0.000 0.000 1.000
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
Beginning Time: 23:06:31
Ending Time: 23:06:54
Elapsed Time: 00:00:23
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